Deep Spatiotemporal Clustering: A Temporal Clustering Approach for Multi-dimensional Climate Data

Clustering high-dimensional spatiotemporal data using an unsupervised approach is a challenging problem for many data-driven applications. Existing state-of-the-art methods for unsupervised clustering use different similarity and distance functions but focus on either spatial or temporal features of the data. Concentrating on joint deep representation learning of spatial and temporal features, we propose Deep Spatiotemporal Clustering (DSC), a novel algorithm for the temporal clustering of high-dimensional spatiotemporal data using an unsupervised deep learning method. Inspired by the U-net architecture, DSC utilizes an autoencoder integrating CNN-RNN layers to learn latent representations of the spatiotemporal data. DSC also includes a unique layer for cluster assignment on latent representations that uses the Student's t-distribution. By optimizing the clustering loss and data reconstruction loss simultaneously, the algorithm gradually improves clustering assignments and the nonlinear mapping between low-dimensional latent feature space and high-dimensional original data space. A multivariate spatiotemporal climate dataset is used to evaluate the efficacy of the proposed method. Our extensive experiments show our approach outperforms both conventional and deep learning-based unsupervised clustering algorithms. Additionally, we compared the proposed model with its various variants (CNN encoder, CNN autoencoder, CNN-RNN encoder, CNN-RNN autoencoder, etc.) to get insight into using both the CNN and RNN layers in the autoencoder, and our proposed technique outperforms these variants in terms of clustering results.

The Backpropagation algorithm for a math student

A Deep Neural Network (DNN) is a composite function of vector-valued functions, and in order to train a DNN, it is necessary to calculate the gradient of the loss function with respect to all parameters. This calculation can be a non-trivial task because the loss function of a DNN is a composition of several nonlinear functions, each with numerous parameters. The Backpropagation (BP) algorithm leverages the composite structure of the DNN to efficiently compute the gradient. As a result, the number of layers in the network does not significantly impact the complexity of the calculation. The objective of this paper is to express the gradient of the loss function in terms of a matrix multiplication using the Jacobian operator. This can be achieved by considering the total derivative of each layer with respect to its parameters and expressing it as a Jacobian matrix. The gradient can then be represented as the matrix product of these Jacobian matrices. This approach is valid because the chain rule can be applied to a composition of vector-valued functions, and the use of Jacobian matrices allows for the incorporation of multiple inputs and outputs. By providing concise mathematical justifications, the results can be made understandable and useful to a broad audience from various disciplines.